/*---------------------------------------------------------------------------*\
  =========                 |
  \\      /  F ield         | foam-extend: Open Source CFD
   \\    /   O peration     | Version:     4.1
    \\  /    A nd           | Web:         http://www.foam-extend.org
     \\/     M anipulation  | For copyright notice see file Copyright
-------------------------------------------------------------------------------
License
	This file is part of foam-extend.

	foam-extend is free software: you can redistribute it and/or modify it
	under the terms of the GNU General Public License as published by the
	Free Software Foundation, either version 3 of the License, or (at your
	option) any later version.

	foam-extend is distributed in the hope that it will be useful, but
	WITHOUT ANY WARRANTY; without even the implied warranty of
	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
	General Public License for more details.

	You should have received a copy of the GNU General Public License
	along with foam-extend.  If not, see <http://www.gnu.org/licenses/>.

Description
	RBF interpolation templates

Author
	Frank Bos, TU Delft.  All rights reserved.
	Dubravko Matijasevic, FSB Zagreb.

\*---------------------------------------------------------------------------*/

#include "RBFInterpolation.H"

// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //

template<class Type>
Foam::tmp<Foam::Field<Type> > Foam::RBFInterpolation::interpolate
(
	const Field<Type>& ctrlField
) const
{
	// HJ and FB (05 Jan 2009)
	// Collect the values from ALL control points to all CPUs
	// Then, each CPU will do interpolation only on local dataPoints_

	if (ctrlField.size() != controlPoints_.size())
	{
		FatalErrorIn
		(
			"tmp<Field<Type> > RBFInterpolation::interpolate\n"
			"(\n"
			"    const Field<Type>& ctrlField\n"
			") const"
		)   << "Incorrect size of source field.  Size = " << ctrlField.size()
			<< " nControlPoints = " << controlPoints_.size()
			<< abort(FatalError);
	}

	tmp<Field<Type> > tresult
	(
		new Field<Type>(dataPoints_.size(), pTraits<Type>::zero)
	);

	Field<Type>& result = tresult();

	// FB 21-12-2008
	// 1) Calculate alpha and beta coefficients using the Inverse
	// 2) Calculate displacements of internal nodes using RBF values,
	//    alpha's and beta's
	// 3) Return displacements using tresult()

	const label nControlPoints = controlPoints_.size();
	const scalarSquareMatrix& mat = this->B();

	// Determine interpolation coefficients
	Field<Type> alpha(nControlPoints, pTraits<Type>::zero);
	Field<Type> beta(4, pTraits<Type>::zero);

	for (label row = 0; row < nControlPoints; row++)
	{
		for (label col = 0; col < nControlPoints; col++)
		{
			alpha[row] += mat[row][col]*ctrlField[col];
		}
	}

	if (polynomials_)
	{
		for
		(
			label row = nControlPoints;
			row < nControlPoints + 4;
			row++
		)
		{
			for (label col = 0; col < nControlPoints; col++)
			{
				beta[row - nControlPoints] += mat[row][col]*ctrlField[col];
			}
		}
	}

	// Evaluation
	scalar t;

	// Algorithmic improvement, Matteo Lombardi.  21/Mar/2011

	forAll (dataPoints_, flPoint)
	{
		// Cut-off function to justify neglecting outer boundary points
		t = (mag(dataPoints_[flPoint] - focalPoint_) - innerRadius_)/
			(outerRadius_ - innerRadius_);

		if (t >= 1)
		{
			// Increment is zero: w = 0
			result[flPoint] = 0*result[flPoint];
		}
		else
		{
			// Full calculation of weights
			scalarField weights =
				RBF_->weights(controlPoints_, dataPoints_[flPoint]);

			forAll (controlPoints_, i)
			{
				result[flPoint] += weights[i]*alpha[i];
			}

			if (polynomials_)
			{
				result[flPoint] +=
					beta[0]
				  + beta[1]*dataPoints_[flPoint].x()
				  + beta[2]*dataPoints_[flPoint].y()
				  + beta[3]*dataPoints_[flPoint].z();
			}

			scalar w;

			if (t <= 0)
			{
				w = 1.0;
			}
			else
			{
				w = 1 - sqr(t)*(3 - 2*t);
			}

			result[flPoint] = w*result[flPoint];
		}
	}

	return tresult;
}


// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

